Analytic asymptotic performance of topological codes

@article{Fowler2013AnalyticAP,
  title={Analytic asymptotic performance of topological codes},
  author={Austin G. Fowler},
  journal={Physical Review A},
  year={2013},
  volume={87},
  pages={040301}
}
  • A. Fowler
  • Published 7 August 2012
  • Physics
  • Physical Review A
Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to simulate the performance of such codes at low p, yet this is a regime we wish to study as low physical error rates lead to low qubit overhead. We present a very general method of analytically estimating the low p performance of the most promising class of… 

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References

SHOWING 1-10 OF 18 REFERENCES
New
and A
  • Rabbani, arXiv:1202.6111
  • 2012
Phys
  • Rev. Lett. 108, 180501
  • 2012
Phys
  • Rev. X 2, 031007
  • 2012
and L
  • C. L. Hollenberg, arXiv:1202.5602
  • 2012
New J
  • Phys. 13, 073043
  • 2011
Phys
  • Rev. A 83, 020302(R)
  • 2011
New J
  • Phys. 12, 033031
  • 2010
and 4 M
  • A. Martin-Delgado, Phys. Rev. A 81, 012319
  • 2010
Phys
  • Rev. E 80, 011141
  • 2009
...
1
2
...